Propagation properties of anomalous hollow vortex beam in uniaxial crystal orthogonal to the optical axis

The analytical equation of an anomalous hollow vortex beam propagating in a uniaxial crystal orthogonal to the optical axis is derived, and the intensity and phase properties of this beam propagating in the uniaxial crystal are illustrated using numerical examples. The influences of topological charge M and the ratio of refractive index n_e/n_o of a uniaxial crystal on the normalized intensity distribution and phase distribution for anomalous hollow vortex beam are discussed and analyzed in detail.